Adding Keyframes to Evaluation-Time Using Python
actually you must see where is each property
the current  API show that is a main property of all shapekeys
in this case:
bpy.context.active_object.data.shape_keys.keyframe_insert(data_path='eval_time', frame=1)

this is different for example of &quot;value&quot;, that is a specific float in each keyblock
bpy.context.active_object.data.shape_keys.key_blocks['Key 1'].keyframe_insert(data_path='value', frame=1)